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<h1><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Metabolic
network reconstruction</span></h1>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'>KEGG
has produced gene annotation files for most sequenced organisms which can be
download from its ftp (</span><span style='font-family:"Times New Roman","serif"'><a
href="ftp://ftp.genome.jp/pub/kegg/genes/organisms">ftp://ftp.genome.jp/pub/kegg/genes/organisms</a>).
For metabolic network reconstruction, the most useful files are those
containing the gene-KO (KEGG orthology) and gene-EC relationships. Based on
these relationships and the reaction-KO, reaction-EC relationships obtained
from the Reaction file (<a
href="ftp://ftp.genome.jp/pub/kegg/ligand/reaction/reaction">ftp://ftp.genome.jp/pub/kegg/ligand/reaction/reaction</a>),
one can easily get the metabolic network (represented as a reaction list and
the corresponding enzyme coding genes) for a specific genome. There could be
some differences between a network obtained by KO based method and an EC based
network. For example, many genes are annotated as enzymes with unclear EC
numbers (1.-.-.-) and the exact reactions catalyzed by these genes are not
clear. However, through the gene-KO, reaction-KO relationships we may find the
exact reactions for them. To get a more complete network, the users are
recommended to create a merged network generated from both methods.</span></p>

<h1><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Metabolic
network analysis</span></h1>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'>For
large scale genome based metabolic networks, there are mainly two types of
analysis methods: (1) stoichiometric matrix based methods such as <a
href="http://en.wikipedia.org/wiki/Flux_balance_analysis">flux balance analysis</a>
(FBA); (2) graph theory based structural analysis methods. </span></p>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Flux
balance analysis is a popular tool for functional analysis of genome scale
metabolic networks. However for FBA one needs to add extra transport/exchange
reactions and choose which metabolites are external metabolites. These
processes are not straight forward from the KEGG based metabolic networks.
Therefore this web tool is focused on graph theory based structural analysis
methods.</span></p>

<h2><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Graph
representation of metabolic network</span></h2>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Graph
theory based methods are mainly used to examine the system level organization
of metabolic networks. A graph is a simplified representation of metabolic
networks. For example, reaction: A+B=C+D can be represented as a graph
including four metabolic links: A-C, A-D, B-C and B-D. Many reactions
include the so called currency metabolites such as H2O, CO2 and ATP. Links
through currency metabolites in a metabolic graph may lead to biological
meaningless pathways. For example, in the glycolysis pathway if ADP is included
in the graph we may get a two step path from glucose to pyruvate via ADP as
shown in the figure. To obtain a metabolic graph which captures the true
biological connectivity, the connections through currency metabolites should be
excluded. Two approaches are used in this web tool. One is based on the metabolic
connection database compiled by Ma and Zeng, <a
href="http://bioinformatics.oxfordjournals.org/cgi/content/abstract/19/2/270">Bioinformatics,
19:270</a>. In this database, the reactions were manually examined to determine
which metabolic connections should be included. Another is based on the <a
href="http://www.genome.jp/kegg/reaction/">KEGG Rpair</a> database. For each
reaction, only the "main" Rpairs (those appeared in the KEGG pathway maps) are
considered. </span></p>

<h2><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Network
structure analysis</span></h2>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Many
structure features of the reconstructed metabolic networks can be calculated
using the web tool. A brief description of the network structure properties can
be seen below and links for detail description in Wikipedia are provided.</span></p>

<p class=MsoNormal><b><span lang=EN-GB style='font-family:"Times New Roman","serif"'></span></b><b><span
style='font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Degree_(graph_theory)">Connection Degree</a></span></b><span
lang=EN-GB style='font-family:"Times New Roman","serif"'>: the number of links
connected with a node. In a directed network, there are in degree and out
degree considering the direction of the links. Nodes with high degree are often
important nodes in a network.</span></p>

<p class=MsoNormal><b><span style='font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Degree_distribution">Degree distribution</a>:
</span></b><span style='font-family:"Times New Roman","serif"'>the distribution
of node degrees in a network. Many complex networks including metabolic
networks are <a href="http://en.wikipedia.org/wiki/Scale-free_networks">scale
free networks</a> which have power law degree distribution.</span></p>

<p class=MsoNormal><b><span style='font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Average_path_length">Average Path Length</a>:
</span></b><span style='font-family:"Times New Roman","serif"'>path length is
defined as the<b> </b>number of the steps in the shortest paths from one node
to another in a graph. The average path length is the average of the path
lengths for all connected pairs of nodes in a graph. </span></p>

<p class=MsoNormal><b><span style='font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Centrality">Centrality</a></span></b><span
style='font-family:"Times New Roman","serif"'>: Closeness Centrality: measure
how close is a node to other connected nodes</span><span lang=EN-GB
style='font-family:"Times New Roman","serif"'>. Betweenness centrality: </span><span
style='font-family:"Times New Roman","serif"'>the fraction of shortest paths
between pairs of nodes that passes through a given node or edge. Load
centrality: a varied form of betweeness centrality. For detail see Ulrik
Brandes: <a
href="http://www.informatik.uni-konstanz.de/algo/publications/b-vspbc-08.pdf"><span
style='color:windowtext;text-decoration:none'>On Variants of Shortest-Path
Betweenness Centrality and their Generic Computation</span></a>. Social
Networks 30(2):136-145, 2008. </span></p>

<p class=MsoNormal><span lang=EN-GB style='font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Connected_component_(graph_theory)"><b>Connected
component</b>s</a>: </span><span class=apple-style-span><span lang=EN-GB
style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman","serif"'>a</span></span><span
class=apple-style-span><span style='font-size:12.0pt;line-height:115%;
font-family:"Times New Roman","serif"'></span></span><span
class=apple-style-span><span lang=EN-GB style='font-size:12.0pt;line-height:
115%;font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Subgraph" title=Subgraph><span lang=EN-US
style='color:windowtext;text-decoration:none'>subgraph</span></a></span></span><span
class=apple-style-span><span style='font-size:12.0pt;line-height:115%;
font-family:"Times New Roman","serif"'></span></span><span
class=apple-style-span><span lang=EN-GB style='font-size:12.0pt;line-height:
115%;font-family:"Times New Roman","serif"'>in which any two vertices are
connected</span></span><span class=apple-style-span><span style='font-size:
12.0pt;line-height:115%;font-family:"Times New Roman","serif"'></span></span><span
class=apple-style-span><span lang=EN-GB style='font-size:12.0pt;line-height:
115%;font-family:"Times New Roman","serif"'>to each other by</span></span><span
class=apple-style-span><span style='font-size:12.0pt;line-height:115%;
font-family:"Times New Roman","serif"'></span></span><span
class=apple-style-span><span lang=EN-GB style='font-size:12.0pt;line-height:
115%;font-family:"Times New Roman","serif"'><a
href="http://en.wikipedia.org/wiki/Path_(graph_theory)"
title="Path (graph theory)"><span lang=EN-US style='color:windowtext;
text-decoration:none'>paths</span></a>, and which is connected to no additional
vertices. Such a subgraph is strongly connected if the link direction is
considered in a directed graph and is weakly connected if direction is ignored.</span></span><span
lang=EN-GB style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman","serif"'>
</span></p>

<p class=MsoNormal><b><u><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Output/input
domain</span></u></b><span lang=EN-GB style='font-family:"Times New Roman","serif"'>:
the output domain of a node is defined as the set of nodes which can be reached
by the node through paths. The input domain of a node is defined as the set of
nodes which can reach the node through paths.</span></p>

<p class=MsoNormal><b><u><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Bow-tie
structure</span></u></b><span lang=EN-GB style='font-family:"Times New Roman","serif"'>:
A common global level organization structure found in many directed networks.
There are mainly four subsets in a bow-tie structure: giant strongly connected
component, the input, the output and the isolated subsets. For detail see <a
href="http://bioinformatics.oxfordjournals.org/cgi/content/abstract/19/11/1423">Ma
and Zeng, Bioinformatics 19:1423</a>. </span></p>

<h1><span lang=EN-GB style='font-family:"Times New Roman","serif"'>Pathway
analysis and network decomposition</span></h1>

<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>A genome
scale metabolic networks often contains hundreds or thousands of reactions and
it is very difficult to check the biological function for such a large network.
This web tool provides two different ways for function analysis. One is to find
the possible pathways from one metabolite to another and thus to analyze the
metabolic capability. Multiple shortest pathways can be found and visualized
automatically so that the users can easily check the found pathways. </span></p>

<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>Another
way for functional analysis is to decompose the network into several small
functionally somehow independent modules. By visually or statistically
examining the biological function of each module, one can obtain a functional
overview of the whole network. Network decomposition is often a computationally
expensive process. We have developed a new fast decomposition method and made
it available here. Furthermore, the decomposition method can generate
partitions with different numbers of modules rather than just one optimal
partition and thus offer the users more flexibility. </span></p>

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